Details

sample113.0ms

Algorithm

intervals

Results

35.0ms	55×	body	1280	valid
23.0ms	43×	body	640	valid
19.0ms	249×	body	80	nan
13.0ms	121×	body	80	valid
6.0ms	21×	body	320	valid
3.0ms	16×	body	160	valid

simplify5.0ms

Counts

1 → 1

Iterations

Iter	Nodes
3	12
2	12
1	11
0	6

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 31.7b

localize11.0ms

Local error

Found 2 expressions with local error:

2.9b	(log (+ N 1))
4.5b	(- (log (+ N 1)) (log N))

rewrite13.0ms

Algorithm

rewrite-expression-head

Rules

13×	`*-un-lft-identity`
11×	`log-prod`
7×	`add-sqr-sqrt` `pow1`
5×	`log-pow` `add-cube-cbrt`
4×	`log-div` `associate--l+` `distribute-lft-out--`
3×	`add-exp-log` `associate--r+`
2×	`associate--l-` `flip3-+` `add-cbrt-cube` `flip-+` `insert-posit16` `distribute-lft-out` `add-log-exp`
1×	`sub-neg` `flip3--` `diff-log` `rem-log-exp` `flip--` `difference-of-squares`

Counts

2 → 43

Calls

2 calls:

4.0ms	(log (+ N 1))
8.0ms	(- (log (+ N 1)) (log N))

series102.0ms

Counts

2 → 6

Calls

2 calls:

29.0ms	(log (+ N 1))
72.0ms	(- (log (+ N 1)) (log N))

simplify1.4s

Counts

49 → 49

Iterations

Iter	Nodes
4	2935
3	1186
2	414
1	195
0	97

prune478.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.0b

localize22.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (/ 1/3 N) (* N N))
0.2b	(/ 1/2 (* N N))
0.4b	(/ 1/3 N)
12.2b	(+ (/ (/ 1/3 N) (* N N)) (- (/ 1 N) (/ 1/2 (* N N))))

rewrite85.0ms

Algorithm

rewrite-expression-head

Rules

43×	`times-frac`
35×	`*-un-lft-identity`
28×	`add-sqr-sqrt` `add-cube-cbrt`
23×	`add-cbrt-cube` `add-exp-log`
19×	`associate-/l*`
9×	`cbrt-undiv` `div-exp` `add-log-exp`
6×	`div-inv`
5×	`associate-/r*`
4×	`pow1` `insert-posit16`
3×	`clear-num` `frac-2neg` `frac-add` `prod-exp` `cbrt-unprod` `distribute-lft-out`
2×	`associate-+r+` `sum-log` `distribute-lft-out--`
1×	`+-commutative` `associate-+r-` `sub-neg` `flip3-+` `flip3--` `diff-log` `frac-sub` `flip-+` `flip--` `associate-/l/`

Counts

4 → 119

Calls

4 calls:

10.0ms	(/ (/ 1/3 N) (* N N))
6.0ms	(/ 1/2 (* N N))
3.0ms	(/ 1/3 N)
63.0ms	(+ (/ (/ 1/3 N) (* N N)) (- (/ 1 N) (/ 1/2 (* N N))))

series174.0ms

Counts

4 → 12

Calls

4 calls:

77.0ms	(/ (/ 1/3 N) (* N N))
46.0ms	(/ 1/2 (* N N))
17.0ms	(/ 1/3 N)
34.0ms	(+ (/ (/ 1/3 N) (* N N)) (- (/ 1 N) (/ 1/2 (* N N))))

simplify10.7s

Counts

131 → 131

Iterations

Iter	Nodes
3	10343
2	1958
1	541
0	200

prune1.0s

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.0b

localize25.0ms

Local error

Found 4 expressions with local error:

9.0b	(sqrt (+ (/ (/ 1/3 N) (* N N)) (- (/ 1 N) (/ 1/2 (* N N)))))
9.0b	(sqrt (+ (/ (/ 1/3 N) (* N N)) (- (/ 1 N) (/ 1/2 (* N N)))))
12.2b	(+ (/ (/ 1/3 N) (* N N)) (- (/ 1 N) (/ 1/2 (* N N))))
12.2b	(+ (/ (/ 1/3 N) (* N N)) (- (/ 1 N) (/ 1/2 (* N N))))

rewrite344.0ms

Algorithm

rewrite-expression-head

Rules

34×	`*-un-lft-identity`
14×	`add-log-exp`
12×	`frac-add` `sqrt-prod` `distribute-lft-out`
10×	`sqrt-div`
8×	`add-sqr-sqrt` `distribute-lft-out--`
6×	`pow1` `add-cube-cbrt`
4×	`associate-+r+` `sum-log` `flip3-+` `flip3--` `add-cbrt-cube` `add-exp-log` `frac-sub` `flip-+` `insert-posit16` `div-inv` `flip--`
2×	`+-commutative` `rem-sqrt-square` `associate-+r-` `sub-neg` `sqrt-pow1` `pow1/2` `diff-log`

Counts

4 → 88

Calls

4 calls:

112.0ms	(sqrt (+ (/ (/ 1/3 N) (* N N)) (- (/ 1 N) (/ 1/2 (* N N)))))
95.0ms	(sqrt (+ (/ (/ 1/3 N) (* N N)) (- (/ 1 N) (/ 1/2 (* N N)))))
62.0ms	(+ (/ (/ 1/3 N) (* N N)) (- (/ 1 N) (/ 1/2 (* N N))))
73.0ms	(+ (/ (/ 1/3 N) (* N N)) (- (/ 1 N) (/ 1/2 (* N N))))

series211.0ms

Counts

4 → 12

Calls

4 calls:

63.0ms	(sqrt (+ (/ (/ 1/3 N) (* N N)) (- (/ 1 N) (/ 1/2 (* N N)))))
61.0ms	(sqrt (+ (/ (/ 1/3 N) (* N N)) (- (/ 1 N) (/ 1/2 (* N N)))))
45.0ms	(+ (/ (/ 1/3 N) (* N N)) (- (/ 1 N) (/ 1/2 (* N N))))
42.0ms	(+ (/ (/ 1/3 N) (* N N)) (- (/ 1 N) (/ 1/2 (* N N))))

simplify4.8s

Counts

100 → 100

Iterations

Iter	Nodes
3	6285
2	1447
1	328
0	112

prune811.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.0b

localize8.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ (+ 1 N) N)
4.4b	(log (/ (+ 1 N) N))

rewrite22.0ms

Algorithm

rewrite-expression-head

Rules

33×	`*-un-lft-identity`
24×	`times-frac`
19×	`add-sqr-sqrt` `add-cube-cbrt`
16×	`log-prod`
7×	`add-exp-log` `distribute-lft-out`
4×	`add-cbrt-cube` `associate-/l*`
3×	`pow1` `associate-/r*`
2×	`div-exp` `rem-log-exp` `insert-posit16` `div-inv` `add-log-exp` `associate-/l/`
1×	`cbrt-undiv` `log-div` `clear-num` `frac-2neg` `flip3-+` `log-pow` `flip-+`

Counts

2 → 62

Calls

2 calls:

14.0ms	(/ (+ 1 N) N)
3.0ms	(log (/ (+ 1 N) N))

series118.0ms

Counts

2 → 6

Calls

2 calls:

72.0ms	(/ (+ 1 N) N)
46.0ms	(log (/ (+ 1 N) N))

simplify2.2s

Counts

68 → 68

Iterations

Iter	Nodes
4	5195
3	1441
2	492
1	223
0	102

prune585.0ms

Pruning

5 alts after pruning (2 fresh and 3 done)

Merged error: 0.0b

regimes34.0ms

Accuracy

100% (0.0b remaining)

Error of 0.0b against oracle of 0.0b and baseline of 31.1b

bsearch56.0ms

Steps

Iters	Range		Point
8	13.774552749451386	335086.0623706297	7336.587493395303

simplify3.0ms

Iterations

Iter	Nodes
2	21
1	21
0	17

end0.0ms

sample2.9s

Algorithm

intervals

Results

1.0s	1747×	body	1280	valid
550.0ms	7978×	body	80	nan
441.0ms	1250×	body	640	valid
405.0ms	4101×	body	80	valid
138.0ms	605×	body	320	valid
67.0ms	297×	body	160	valid